Carl is boarding a plane. He has $2$ checked bags of equal weight and a backpack that weighs $4 \text{ kg}$. The total weight of Carl's baggage is $35 \text{ kg}$. Write an equation to determine the weight, $w$, of each of Carl's checked bags. Find the weight of each of his checked bags.
Solution: Let $w$ be the weight in kilograms of each checked bag. The weight of Carl's $2$ checked bags is $2w \text{ kg}$. The weight of his backpack is $4\text{ kg}$. The total weight of his baggage is $2w+4\,\text{kg}$. Since his total baggage weighs $35\text{ kg}$, let's set this equal to $35$ : $ 2w+4=35$ Now, let's solve the equation to find the weight of each of his checked bags $(w)$. $\begin{aligned} 2w+4&=35\\ \\ 2w+4{-4}&=35{-4}&&{\text{subtract }4} \text{ from each side}\\ \\ 2w&=31\\ \\ \dfrac{2w}{{2}}&=\dfrac{31}{{2}}&&\text{divide each side by ${2}$}\\ \\ w&=15.5\end{aligned}$ The equation is $2w+4=35$. The weight of each checked bag is $15.5\,\text{kg}$.